Raquel Coelho Simoes, Lancaster University

Simple-mindedness in negative Calabi-Yau cluster categories of the hereditary type

Simple-minded systems were introduced by Koenig-Liu as an abstraction of non-projective simple modules in stable module categories. In this talk, we will consider simple-minded systems in certain orbit categories of the bounded derived category of a hereditary algebra, which can be considered to be negative Calabi-Yau cluster categories. Simple-minded systems in this setting turn out to play the role of cluster-tilting objects in the positive Calabi-Yau setup. We will give a bijection between simple-minded systems, simple-minded collections in the fundamental domain and positive (higher) noncrossing partitions. These results generalise the results of Iyama-Jin for Dynkin type. This is based on joint work with David Pauksztello and David Ploog.